Question: Simplify to lowest terms. $\dfrac{78}{52}$
There are several ways to tackle this problem. What is the greatest common factor (GCD) of 78 and 52? $78 = 2\cdot3\cdot13$ $52 = 2\cdot2\cdot13$ $\mbox{GCD}(78, 52) = 2\cdot13 = 26$ $\dfrac{78}{52} = \dfrac{3 \cdot 26}{ 2\cdot 26}$ $\hphantom{\dfrac{78}{52}} = \dfrac{3}{2} \cdot \dfrac{26}{26}$ $\hphantom{\dfrac{78}{52}} = \dfrac{3}{2} \cdot 1$ $\hphantom{\dfrac{78}{52}} = \dfrac{3}{2}$ You can also solve this problem by repeatedly breaking the numerator and denominator into common factors. For example: $\dfrac{78}{52}= \dfrac{2\cdot39}{2\cdot26}= \dfrac{2\cdot 13\cdot3}{2\cdot 13\cdot2}= \dfrac{3}{2}$